How do I rotate an object in an anti gravity simulation?
This was done in Version 2.77a and should work in 2.8+ .  (Blend file below)
There's very little to do to get this working in Blender...
.
First up, make sure the physics cache has enough frames set up to accommodate the action.
What makes this work is the 'natural' dislike' physics objects have for each other.  They don't like being together and even with the collision margin set to 0.002, they'll still want to move apart in a no-gravity situation.
So all you need to do is place two objects together and switch on the physics.
Details -
The (invisible) cube is a rigid body with physics set to 'Active'  and it's ' Animated' box ticked permanently.
It's not keyframed and left stationary.
The black (floating) object is also a rigid body and left stationary but still set to 'Active' and with it's physics keyframed to 'Animated' at frame 1. That's switched to 'Dynamic' at the frame the hand in the video is to touch it, or it is to be hit by another floating object.
When the collision isn't matched to a video'd object, normal physics should apply when they hit.  Both objects could be animated and switched to Dynamic at the collision point
The forces at play as shown above are from the physics engine only.  With the cube barely touching the floater, and 'Collision Margin' set to 0.002 (on them both) the repelling force between them isn't great and it gently drifts away.
How it drifts and the force behind it would depend on the angle and penetration of the cube.
The floater will want to slow down over time so the damping settings (physics) have to be set to zero.
Similarly the shape selection on both, 'Convex Hull' as against 'Mesh' will also make a difference.
'Passive' and 'Active' choices can also have a marked effect.
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If you have 3D objects in the workspace drifting and colliding, normal physics would take care the impact mechanations.
If on the other hand you want to control the angle and at what speed the 'victim' object takes off, the described example above would do that.  The visible colliding object wouldn't need physics.  It would be animated scenery only and would have no effect on those with physics properties.